Module 8 - 4th QUARTER - ZNNHS

Republic of the Philippines

Department of Education Regional Office IX, Zamboanga Peninsula

Zest for Progress

Zeal of Partnership

8

4th QUARTER – Module 8: PROBABILITY OF A SIMPLE EVENT

Name of Learner: ___________________________

Grade & Section: ___________________________

Name of School: ___________________________

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Mathematics – Grade 8 Alternative Delivery Mode Quarter 4 - Module 8: Probability of a Simple Event First Edition, 2020

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Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio

Printed in the Philippines

Department of Education – Region IX, Zamboanga Peninsula

Office Address: Tiguma, Airport Road, Pagadian City

Telefax: (062) – 215 – 3751; 991 – 5975

E-mail Address: [email protected]

Development Team of the Module

Writer: Feberto L. Montealegre

Editors: Maria Fe S. Gadaingan

Roda S. Buenaventura

Reviewers: EPS, Mathematics Vilma A. Brown, Ed. D.

Principal Garry D. Sta. Ana

Management Team: SDS Roy C. Tuballa, EMD, JD, CESO VI

ASDS Jay S. Montealto, CESO VI

ASDS Norma T. Francisco, DM, CESE

EPS Mathematics Vilma A. Brown, Ed. D.

EPS LRMS Aida F. Coyme, Ed. D.

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Introductory Message

This Self – Learning Module (SLM) is prepared so that you, our dear learners, can continue

your studies and learn while at home. Activities, questions, directions, exercises, and

discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you

discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will

tell you if you can proceed on completing this module or if you need to ask your facilitator or

your teacher’s assistance better understanding of the lesson. At the end of each module,

you need to answer the post-test to self-check your learning. Answer keys are provided for

each activity and test. We trust that you will be honest in using these.

In addition to the material in the main text, notes to the Teacher are also provided to our

facilitators and parents for strategies and reminders on how they can best help you on your

home-based learning.

Please use this module with care. Do not put unnecessary marks on any part of this SLM.

Use a separate sheet of paper in answering the exercises and tests. Read the instructions

carefully before performing each task.

If you have any questions in using this SLM or any difficulty in answering the tasks in this

module, do not hesitate to consult your teacher or facilitator.

Thank you.

This module introduces the very basic of simple probability or the likelihood

that a single event will occur.

This module will assess what you have learned on the basic mathematical

concepts and your skills in performing the different mathematical operations that

may help you understand the lesson on probability.

Through this module, you are expected to find the probability of a simple

event. (M8GE-IVh-1)

What I Need to Know

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What I Know

Directions: Read and understand each item carefully. Write the letter of the correct

answer on a separate sheet.

1. What is the probability of picking not a heart in a deck of 52 cards?

a. 3

4 b.

1

4 c.

2

11 d.

1

8

2. If you throw a three dice, what is the probability that you do not throw any 4’s, 5’s

or 6’s?

a. 1

2 b.

1

4 c.

1

8 d.

3

4

3. A bag contains 10 marbles numbered 1 to 10. What is the probability of selecting

an even number?

a. 1

4 b.

1

2 c.

1

3 d.

1

8

4. If you spin a spinner, what is the probability that the point will land on A?

a. 1

2 c.

3

4

b. 1

4 d.

1

3

5. A single die is tossed. What is the probability of a number greater than 3?

a. 1

4 b.

1

2 c.

1

3 d.

3

4

LESSON

1 Probability of a Simple Event

What’s In

Directions: Complete the table below and answer the questions that follow. Write

your answers on a sperate sheet. (Note: No same outcome is allowed.)

EXPERIMENT: Rolling two dice.

A A O O

A A

D

F

4

1 2 3 4 5 6

1 1,1

2 2,1 2,5

3 3,1 3,2

4 4,1 4,4

5 5,1

6 6,1 6,6

a. How many possible outcomes in rolling a die? b. List down all the possible outcomes. c. Rolling two dice together, how many possible outcomes are there?

What’s New

Directions: Complete the table and answer the questions that follow. Write your

answers on a sperate sheet.

A jar contains of 11 red balls, 7 green balls, 6 blue balls and 8 yellow

balls. What is the probability of picking:

Colors Probability of an event

a red

a blue

a yellow

a green

a. How many balls are there in the jar?

b. What is the probability when you are to select yellow or blue color?

c. What is the probability of picking Red or green?

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What is It

Observe the given examples below.

➢ Probability of a simple event, P (event), is a number from 0 to 1

which tells how likely the event is to happen.

➢ When finding the probability of an event occurring, we will use the

formula: number of favorable outcomes over the number of total

outcomes. In symbols,

𝑷ሺ𝑬ሻ =𝒏ሺ𝑬ሻ

𝒏ሺ𝑺ሻ

where 𝒏ሺ𝑬ሻ represents the favorable outcomes and 𝒏ሺ𝑺ሻ is the total

number of possible outcomes.

PROBABILITY OF SIMPLE EVENT

1. The probability of any event is a number (either in fraction, in decimal or

in percent) from 0 to 1.

2. If an event will never happen, then its probability is 0.

3. If the event is sure to happen, then the probability is 1.

4. The sum of the probabilities of all the outcomes in the sample space is 1.

PROBABILITY RULES T

What is the probability of obtaining an even number in rolling a die once?

SOLUTION:


𝒏ሺ𝑺ሻ

ሼ𝟐, 𝟒, 𝟔ሽ

ሼ𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔ሽ

= 3

6

= 1

2 Decimal: 0.50 Percent: 50%

EXAMPLE 1.

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Find the probability of getting a head when tossing a coin.

SOLUTION:


𝒏ሺ𝑺ሻ

ሼ𝑯ሽ

ሼ𝑯, 𝑻ሽ

= 1


EXAMPLE 2.

What is the probability of getting a DIAMOND in a deck of cards?

SOLUTION:


𝒏ሺ𝑺ሻ

ሼ𝟏𝟑ሽ

ሼ𝟓𝟐ሽ

= 13

52 or

1


EXAMPLE 3.

A pack of buttons has 2 white buttons, 3 red buttons, 4 black buttons and 1

yellow button. If a button is picked at random, what is the probability that the

button picked is black?

SOLUTION:


𝒏ሺ𝑺ሻ

ሼ𝟒ሽ

ሼ𝟐 + 𝟑 + 𝟒 + 𝟏ሽ

= 4

10 or

2


EXAMPLE 4.

There are 28 girls and 12 boys in a class. If a student is selected at random,

what is the probability that the student selected is a girl?

SOLUTION:

𝑃ሺ𝐸ሻ = 𝑛ሺ𝐸ሻ

𝑛ሺ𝑆ሻ

ሼ28ሽ

ሼ28+12ሽ

= 28

40 or

7


EXAMPLE 5.

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What’s More

Directions: Find the probability of an event.

1. What is the probability of getting 6 in rolling a die? 2. The spinner shown on the right is spun once. Determine the probability of the

following:

a. P(F)

b. P(vowels)

c. P(D or G)

d. P(consonants)

3. There are 7 green marbles, and 5 black marbles. If one marble is chosen at

random, find

a. P(green)

b. P(black)

What I Have Learned

Directions: Construct a table and determine the probability of a simple event.

If you rolled a two dice simultaneously, find the probability of the following:

a. a sum of 7

b. a sum of 12

c. a sum of less than 10

d. a double number

e a sum of greater than 5

J A

B

C D E

F

G

H

I

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What I Can Do

Directions: Match the following with each letter on the probability line. Write your

answer on a separate sheet.

A B C D E Impossible Unlikely Even Chance Likely Certain 0 0.25 0.5 0.75 1 EXAMPLE: ___E___ There are 12 months in a year. 1. In Zamboanga Peninsula, it will snow in May.

2. Out of 20 items, Mario got 15.

3. The day before Tuesday is Monday.

4. Of the 40 chickens, only 10 survived.

5. If you flip a coin, the result is tail.

6. The fourth person to knock on the door will be a girl.

7. All months of the year have 28 days.

8. Next year, the month after March has 30 days.

9. The chance that the last outcome in rolling a number cube is an even number.

10. There are 7 days in a week.

Assessment

Directions: Read each item carefully. Choose the letter of the correct answer and write it on a separate sheet. 1. If a letter is chosen at random from the word MATHEMATICS, what is the

probability that the letter chosen is A?

a. 2

11 b.

2

5 c.

1

11 d.

3

4

2. Of the 90 freshmen students, 50 are girls. If a student is selected at random for a

vacation. What is the probability of selecting a boy?

a. 3

5 b.

4

9 c.

2

5 d.

1

5

3. When rolling a die, what is the probability of rolling a 3?

a. 3

5 b.

2

5 c.

1

6 d.

5

6

9

4. The spinner at the right is spun once. Determine the

probability of getting a red.

a. 1

2 c.

3

10

b. 3

5 d.

1

10

5. There are 5 green, 7 blue and 3 red pens. If one ballpen is chosen at random,

then what is the probability of getting a red pen?

a. 2

5 b.

4

5 c.

1

5 d.

1

15

6. A coin is tossed 3 times, what is the probability that at least one head is

obtained.

a. 7

8 b.

1

8 c.

1

5 d.

1

6

7. Find the probability of getting a numbered card when a card is drawn

from a pack of 52 cards?

a. 9

13 b.

1

13 c.

4

13 d.

7

13

8. What is the probability of getting a sum of 7 when rolling two dice?

a. 5

6 b.

1

6 c.

7

6 d.

1

2

9. Which of the following statement is TRUE?

a. Flipping a coin thrice has 3 possible outcomes.

b. The probability of rolling 5 in a die is 1/6.

c. The probability of rolling 7 in a die is 1/7.

d. none of the above.

10. A box contains 50 orange, pink, black and brown balls. The probability of drawing

a single pink ball at random is 1/5. What does it mean?

a. There are 5 pink balls in the box.

b. There are 10 pink balls in the box.

c. There are more pink balls than the others.

d. There is only one pink ball in the box.

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Answer Key

References:

Emmanuel P. Abuzo,et.al., Mathematics-Grade 8 (Learner’s Module) First Edition,

Pasig City: Department of Education-Instructional Materials Council Sectretariat

(DepEd-IMCS),2013, 568-569.

What I Know:

1. A 3. B 5. B

2. C 4. A

What’s In:

1. 6 outcomes 2. { 1, 2, 3, 4, 5, 6 } 3. 36 outcomes

What’s New:

1. 32 2. 7

16 3.

9

16

What’s More:

1. 1

6 2. a.

1

10 c.

1

5 3. a.

7

12 b.

5

12

b. 3

10 d.

7

10

What I Have Learned:

1. 𝟏

𝟔 2.

𝟏

𝟑𝟔 3.

𝟓

𝟔 4.

𝟏

𝟔 5.

𝟏𝟑

𝟏𝟖

What I Can Do:

1. A 3. E 5. C 7. E 9. C

2. D 4. B 6. C 8. E 10. E

Assessment:

1. A 3. C 5. C 7. A 9. B

2. B 4. A 6. A 8. B 10. B

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I AM A FILIPINO

by Carlos P. Romulo

I am a Filipino – inheritor of a glorious past, hostage to the

uncertain future. As such, I must prove equal to a two-fold

task – the task of meeting my responsibility to the past, and

the task of performing my obligation to the future.

I am sprung from a hardy race – child many generations

removed of ancient Malayan pioneers. Across the centuries,

the memory comes rushing back to me: of brown-skinned

men putting out to sea in ships that were as frail as their

hearts were stout. Over the sea I see them come, borne upon

the billowing wave and the whistling wind, carried upon the

mighty swell of hope – hope in the free abundance of the

new land that was to be their home and their children’s

forever.

This is the land they sought and found. Every inch of shore

that their eyes first set upon, every hill and mountain that

beckoned to them with a green and purple invitation, every

mile of rolling plain that their view encompassed, every

river and lake that promised a plentiful living and the

fruitfulness of commerce, is a hollowed spot to me.

By the strength of their hearts and hands, by every right of

law, human and divine, this land and all the appurtenances

thereof – the black and fertile soil, the seas and lakes and

rivers teeming with fish, the forests with their inexhaustible

wealth in wild and timber, the mountains with their bowels

swollen with minerals – the whole of this rich and happy

land has been for centuries without number, the land of my

fathers. This land I received in trust from them, and in trust

will pass it to my children, and so on until the world is no

more.

I am a Filipino. In my blood runs the immortal seed of

heroes – seed that flowered down the centuries in deeds of

courage and defiance. In my veins yet pulses the same hot

blood that sent Lapulapu to battle against the alien foe, that

drove Diego Silang and Dagohoy into rebellion against the

foreign oppressor.

That seed is immortal. It is the self-same seed that flowered

in the heart of Jose Rizal that morning in Bagumbayan

when a volley of shots put an end to all that was mortal of

him and made his spirit deathless forever; the same that

flowered in the hearts of Bonifacio in Balintawak, of

Gregorio del Pilar at Tirad Pass, of Antonio Luna at

Calumpit, that bloomed in flowers of frustration in the sad

heart of Emilio Aguinaldo at Palanan, and yet burst forth

royally again in the proud heart of Manuel L. Quezon when

he stood at last on the threshold of ancient Malacanang

Palace, in the symbolic act of possession and racial

vindication. The seed I bear within me is an immortal seed.

It is the mark of my manhood, the symbol of my dignity as

a human being. Like the seeds that were once buried in the

tomb of Tutankhamen many thousands of years ago, it

shall grow and flower and bear fruit again. It is the insigne

of my race, and my generation is but a stage in the

unending search of my people for freedom and happiness.

I am a Filipino, child of the marriage of the East and the

West. The East, with its languor and mysticism, its

passivity and endurance, was my mother, and my sire was

the West that came thundering across the seas with the

Cross and Sword and the Machine. I am of the East, an

eager participant in its struggles for liberation from the

imperialist yoke. But I know also that the East must awake

from its centuried sleep, shake off the lethargy that has

bound its limbs, and start moving where destiny awaits.

For I, too, am of the West, and the vigorous peoples of the

West have destroyed forever the peace and quiet that once

were ours. I can no longer live, a being apart from those

whose world now trembles to the roar of bomb and cannon

shot. For no man and no nation is an island, but a part of

the main, and there is no longer any East and West – only

individuals and nations making those momentous choices

that are the hinges upon which history revolves. At the

vanguard of progress in this part of the world I stand – a

forlorn figure in the eyes of some, but not one defeated

and lost. For through the thick, interlacing branches of

habit and custom above me I have seen the light of the

sun, and I know that it is good. I have seen the light of

justice and equality and freedom, my heart has been lifted

by the vision of democracy, and I shall not rest until my

land and my people shall have been blessed by these,

beyond the power of any man or nation to subvert or

destroy.

I am a Filipino, and this is my inheritance. What pledge

shall I give that I may prove worthy of my inheritance? I

shall give the pledge that has come ringing down the

corridors of the centuries, and it shall be compounded of

the joyous cries of my Malayan forebears when first they

saw the contours of this land loom before their eyes, of the

battle cries that have resounded in every field of combat

from Mactan to Tirad Pass, of the voices of my people

when they sing:

“I am a Filipino born to freedom, and I shall not rest until

freedom shall have been added unto my inheritance—for

myself and my children and my children’s children—

forever.”

Module 8 - 4th QUARTER - ZNNHS

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